Let's assume the dairy needs x gallons of milk containing 6% butterfat and y gallons of milk containing 1% butterfat to obtain the desired 270 gallons of milk.
Given:
Total volume of milk needed = 270 gallons
Butterfat percentage desired = 4%
To solve this problem, we can set up a system of equations based on the amount of butterfat in each type of milk.
Equation 1: For butterfat content
0.06x + 0.01y = 0.04 * 270
Equation 2: For total volume
x + y = 270
Now we can solve the system of equations to find the values of x and y.
Using Equation 2, we can express x in terms of y:
x = 270 - y
Substituting this value of x into Equation 1:
0.06(270 - y) + 0.01y = 0.04 * 270
16.2 - 0.06y + 0.01y = 10.8
Combining like terms:
-0.05y = -5.4
Dividing by -0.05:
y = 108
Substituting the value of y back into Equation 2:
x + 108 = 270
x = 162
Therefore, to obtain the desired 270 gallons of milk containing 4% butterfat, the dairy needs 162 gallons of milk containing 6% butterfat and 108 gallons of milk containing 1% butterfat.